As a full time chess teacher and coach, I see this type of situation arise quite a bit! Often when it looks like a player is about to be mated, the player being attacked panics and doesn't look at the entire board. I'll try to write this without giving away the solution:

When a mating attack comes our way, we tend to focus on directly on the pieces attacking our King and the pieces we have immediately in the vicinity of the attack. Rather than look for simple solutions, many players look for more complex ways to get out of the attack. I suggest to my students the following:

1. Emotionally detatch yourself from the situation. Look at the position as if it were a positional puzzle from someone else's game. This allows you to use a more balanced analytical thought process.

2. Go through the basic ABC checklist for the King; A = Avoid (can you more out of the attack). B = Block (can you block the attack). C = Capture (can you capture the attacker).

3. Do a positional survey of your pieces and pawns. This is important. Because you're concentrating on the area close to the mating attack, you can miss a piece that can come to your aid.

The solution to the problem presented in this post is a great example of finding a creative solution to potential mate. Thank you very much for posting it!

There are more than two moves that keep white in a winning position. I can't see why white would lose after Bxh6, for example.

Of course, Qa3 and Bf4 are the obvious moves, but technically speaking, white can also sacrifice his queen with Qxd8+ and Qxc7+, and, due to his material advantage, still get a win. It's a little bit of an innacuraccy to say that white has only two options here that keep the win, because other moves do that as well, even though they are not as good.

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